Suppose that X is a N(3,4) random variable and suppose that Y=2X-1. Determine P(Y>8).
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- Given X~B(6, 0.55) and Y = y 1 P(Y = y) 0.3 2 0.3 3 0.4 And these random variables are independent of one another. What is P(X + Y≥ 3) 0.023 0.977 0.915 0.979 0.945 No answerI roll a fair die twice and obtain two numbers: X1 = result of the first roll, and X2 = result of the second roll. Write down the sample space S, and assuming that all outcomes are equally likely (because the die is fair), find the probability of the event A defined as the event that X1 + X2 = 8.Let X be a binomial random variable with parameters of 9 and 0.1. Let Y be a binomial random variable with parameters of 6 and 0.3. Assume X and Y are independent. Then the probability that X + Y = 2 equals Preview
- Three balls are selected from a bag that contains 3 blue, 2 green, and 5 yellow balls. Here, we define random variables as B = number of blue balls drawn, G = number of green balls drawn, Y = number of yellow balls drawn. Please list the following values:Q1:Show that: If X1, X2, , Xn are independent random variables and X = X1 + X2 ++Xn, then Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a die? Q3: Find the expectation and the variance of X, where X is binomial random variable X - Binomial (n, p), Var(X)? 1 Chapter 3 Let X be a discrete random variable with range Rx = {1, 2, 3, ...}. Q4: Suppose the PMF of X is given by 1 for k = 1, 2, 3, ... 2k Px (k) = a) Find and plot the CDF of X, Fx (a). b) Find P(1 < X < 3). Chapter 3 Functions of Random Variables Q5: Example. Let Rx = {0, T T 37 , such that 4'2 4. Find E[sin(X)]. Q6: A machine produces a defected items with a probability of 0.1. What is the probability that in a sample of three item will have at most one item defected? Q7: For any independent X, and Y random variables, E[XY]=E[X]E[Y]. Show that? Q8: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2. 3 Chapter 3Let X denote the number of bits received in error in a digital communication channel, and assume that X is a binomial random variable with p = 0.01. If 100 bits are transmitted, then P(X>1)=
- please send correct answer Q6Suppose that X is a random variable * ? having the following m.g.f., Find Var(x) 7t_e4t M, (t) = eT 173 O 5 O 413 O 3148 O 55 OSuppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO
